Okay, reading all this, and I am utterly amazed that nobody thought of this. Let's look at a couple facts, one from the past, the other from, well, the past as well, but more sciency.
First, the Badlands, a place where no mutant powers work. None. That goes for Wolverine's healing factor! Take him there, strand him, and let the super-fauna have a field day. If he makes it to a beach? Have snipers finish the job.
Second, Adamantium is disgustingly poisonous. The only reason he can maintain his health at all is because of his regenerative capabilities. And even then, the adamantium in his system is severely slowing what he's capable of. Without it? Oh, he'd probably regrow a limb instantly after losing it. Now, if we were to compound this with the first point above, then we could strand him in the Badlands and just let the metal kill him. Beautiful!
Of course, now we approach the questions of whether there'd be a second wolverine if you were to remove his head, or sever him in half. The fact is there wouldn't. For his regeneration, most of it is based on the key genomes locked inside of his brain, and thus only the portion with the brain would be able to regenerate. Ripped vertically in half? They would be unable to regenerate until both are back together. (Yes, I'm purposely ignoring his regeneration from a solitary cell)
Now, why does the Adamantium regenerate with his skeleton each time he does so? ...
Well, that's for another fan to pick off. I only know his powers, and their limitations. Not a damn thing about the metalurgy of his enhancements.